In general, (meth)acrylic acid is produced by the following steps:                a gas containing (meth)acrylic acid is obtained by gas-phase oxidation reaction;        the gas is supplied to a condensing tower or a collecting tower to obtain a crude (meth)acrylic acid solution;        (meth)acrylic acid is purified from the crude solution.        
As a purification method for (meth)acrylic acid, crystallization is used as well as distillation, diffusion, extraction and the like.
A gas containing (meth)acrylic acid obtained by gas-phase oxidation reaction contains by-products such as acetic acid and dimer as well as raw material compounds in addition to (meth)acrylic acid. Therefore, it is difficult to obtain (meth)acrylic acid having sufficiently high purity by only one time purification. In addition, it is necessary to combine various purification methods or repeat a purification method.
For example, acrylic acid or the like is crystallized a plurality of times to be purified in Patent Documents 1 and 2. In the processes described in the Patent Documents, tanks for respective crystallization stages are set up and the compounds stored in the respective tanks are used as raw materials for crystallization of the next stage. As the process, when purification by crystallization is repeated a plurality of times, a compound obtained in a stage is prevented from being mixed with a compound obtained in the previous stage since the compound obtained in the previous stage contains impurity in a larger amount. On the other hand, a crystallizer is more complicated in structure and more expensive than a tank; therefore, in general, a crystallizer is not necessarily set up for each crystallization stage although there may be some cases where the number of crystallizers is the same as the number of the repeating times of crystallization. For example, in the figures of Patent Documents 1 and 2, a plurality of tanks are described corresponding to the number of crystallization operations, but only one crystallizer is described.
Under the above-described circumstances, it is required to operate a crystallizer as efficiently as possible. However, there is no description about specific operation condition of a crystallizer for efficiently carrying out crystallization purification in Patent Documents 1 and 2.
In addition, it is general in crystallization purification to not only crystallize (meth)acrylic acid but also to melt the obtained crystal for transportation convenience. Therefore, in a crystallizer, both of a cooling energy for crystallizing (meth)acrylic acid from a crude (meth)acrylic acid solution and a heating energy for melting the (meth)acrylic acid crystal are needed.